Ankara University
Ins tute of Nuclear Sciences
Owner on behalf of Ins tute of Nuclear Sciences,
Ankara University,
Director
Niyazi MERİÇ, Ph.D
Available Online—h p://jns.en.ankara.edu.tr
Editor in Chief
Haluk YÜCEL, Ph.D.Assistant Editor‐in‐Chief
George S. POLYMERIS, Ph.D.Editorial Board
Birol ENGİN, Ph.D. Enver BULUR, Ph.D. Erkan İBİŞ, M.D. Gaye Ö. ÇAKAL, Ph.D. Güneş TANIR, Ph.D. Hamit HANCI, M.D. Ioannis LIRITZIS, Ph.D. İsmail BOZTOSUN, Ph.D. M.Salem BADAWI, Ph.D. Mustafa KARADAĞ, Ph.D. Mustafa YILDIZ, Ph.D. Niyazi MERİÇ, Ph.D. Osman YILMAZ, Ph.D. Özlem BİRGÜL, Ph.D. Özlem KÜÇÜK, M.D. Slobodan JOVANOVIC, Ph.D. Turan OLĞAR, Ph.D.Volume 1, No. 1 January 2014
ISSN: 2148-3981
Journal of Nuclear Sciences
Not for reproduction, distribution or commercial use.
VSRQWDQHRXVILVVLRQRI
&I
0.RXUPR+0$KPDGRY 5.Ro
'HSDUWPHQWRI(QJLQHHULQJ3K\VLFV)DFXOW\RI(QJLQHHULQJ*D]LDQWHS8QLYHUVLW\*D]LDQWHS7XUNH\ 5HFHLYHGUHFHLYHGLQUHYLVHGIRUPDFFHSWHG
$%675$&7
,QWKLVZRUNWKHFRUUHODWLRQKDVEHHQLQYHVWLJDWHGEHWZHHQWKHQHXWURQQXPEHUVDQGDYHUDJHH[FLWDWLRQHQHUJLHV IRU WKH FRPSOHPHQWDU\ ILVVLRQ IUDJPHQWV LQ WKH VSRQWDQHRXV ILVVLRQ RI&I 7KH UHVXOWV RI WKH H[SHULPHQWDO ZRUNRQWKHDYHUDJHQHXWURQQXPEHUWRWDONLQHWLFHQHUJ\GLVWULEXWLRQRIWKHSDLURIIUDJPHQWVDQGWKHDYHUDJH HQHUJLHV RI QHXWURQV DQG JDPPD TXDQWD HPLWWHG IURP WKH ILVVLRQ IUDJPHQWV DUH XVHG &DOFXODWHG UHVXOWV DUH FRPSDUHGZLWKWKHUHVXOWVRIWKHRWKHUFDOFXODWLRQVDQGPHDVXUHPHQWV
.H\ZRUGV1XFOHDUILVVLRQ&IQHXWURQQXPEHUH[FLWDWLRQHQHUJ\FRUUHODWLRQ
,QWURGXFWLRQ
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
7KHRUHWLFDO VWXG\ RI WKH SUREOHP GHSHQGV RQ WKH PRGHO XVHG WR GHVFULEH H[FLWDWLRQ HQHUJ\ GHSHQGHQFHRQQXFOHDUWHPSHUDWXUHXVXDOO\ZLWKLQ
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
$V VWDWHG DERYH LQ WKH VWXG\ RI H[FLWDWLRQ HQHUJ\ SDUWLWLRQEHWZHHQWKHILVVLRQIUDJPHQWVQXPEHURI QHXWURQV HPLWWHG IURP IUDJPHQW LV WKH PDLQ TXDQWLW\ EHFDXVH HDFK HPLWWHG QHXWURQ FDUULHV RXW ̱ሺ െ ሻH[FLWDWLRQHQHUJ\IURPIUDJPHQWDQG WKXV WKH FRQWULEXWLRQ WR WKH IUDJPHQW H[FLWDWLRQ LV PDLQO\ GHWHUPLQHG E\ WKH DYHUDJH QXPEHU RI QHXWURQV \LHOGHG IURP WKH IUDJPHQW RI PDVV QXPEHU $GGLWLRQDOO\ JDPPD HPLVVLRQ FDUULHV WKH HQHUJ\ RI ILVVLRQ IUDJPHQW ZKLFK LV OHVV SUREDEOH FRPSDUHG WR QHXWURQ HPLVVLRQ 7KH UDWLR
Kourmoetal./JournalofNuclearSciences1(2014)6Ͳ12 RI QHXWURQ DQG JDPPD ZLGWKV Ȟ୬ΤȞஓሻLV̱ͳͲଶDW WKH IUDJPHQW H[FLWDWLRQV ̱ DQG DQJXODU PRPHQWXP YDOXHͷ െ >@ 7KXV FRPSHWLWLRQ EHWZHHQQHXWURQDQGJDPPDHPLVVLRQPD\EHYDOLG IRU WKH ODVW QHXWURQ HPLWWHG IURP WKH IUDJPHQW 7KHUHIRUH JDPPD UD\V DUH XVXDOO\ VXSSRVHG WR EH HPLWWHG DIWHU DOO SRVVLEOH QHXWURQ HPLVVLRQV DQG WKHLUFRQWULEXWLRQWRWKHILVVLRQIUDJPHQWH[FLWDWLRQ HQHUJ\ PXVW EH WDNHQ LQWR WKH DFFRXQW IRU WKH DFFXUDWH FDOFXODWLRQ RI ILVVLRQ IUDJPHQW H[FLWDWLRQ HQHUJ\
)LUVWQHXWURQ\LHOGH[SHULPHQWVLQQHXWURQLQGXFHG ILVVLRQ RI ଶଷଷǡଶଷହǡଶଷଽDQG LQ VSRQWDQHRXV
ILVVLRQ RIଶହଶZHUH DQDO\]HG LQ WKH ZRUN RI 7HUUHOO>@DQGUHIHUHQFHVWKHUHLQDQGLWZDVVWDWHG WKDW WKH ORZHVW QXPEHU LQ QHXWURQ HPLVVLRQ FRUUHVSRQGV WR WKH IRUPDWLRQ RI QHDU PDJLF QXFOHL ZLWK FKDUJH DQG QHXWURQ QXPEHUV RI ൎ ͷͲ ൎ ͷͲPDVVHVͺʹDQGͳʹͺ UHVSHFWLYHO\ DQG LW ZDV VXJJHVWHG ³WKDW PDJLF DQG QHDU PDJLF IUDJPHQWV KDYHORZH[FLWDWLRQVDQGFRQVHTXHQWO\HPLWDOPRVW QR QHXWURQV EHFDXVH RI JUHDWHU ULJLGLW\ DJDLQVW GLVWRUWLRQ IURP QHDUVSKHULFDO VKDSHV´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ͳʹ SURWRQLQGXFHGILVVLRQRIଶଷଶPHDVXULQJSULPDU\ DQG VHFRQGDU\ ILVVLRQ IUDJPHQW PDVV \LHOGV DQG WRWDO NLQHWLF HQHUJ\ RI SULPDU\ IUDJPHQWV 3DUW RI WKH UHVXOWV RI WKLV ZRUN ZKLFK ZHUH SUHVHQWHG IRU DV\PPHWULF ILVVLRQ PRGHO DUH XVHG IRU FRPSDULVRQ ZLWK RXU UHVXOWV %HORZ LQ WKH VHFWLRQV GLIIHUHQW LQGHSHQGHQW H[SHULPHQWDO GDWD DQDO\]HG DQG WKHQ SUHVHQWHG RXU SUHVFULSWLRQ IRU FDOFXODWLRQ RI SDUWLWLRQ RI H[FLWDWLRQ HQHUJ\ EHWZHHQ WKH IUDJPHQWV LQ VSRQWDQHRXV ILVVLRQ RI &I 'LVFXVVLRQDQGFRQFOXVLRQDUHJLYHQLQ6HFWLRQͷ
&RUUHODWLRQEHWZHHQWKHDYHUDJHQHXWURQ QXPEHUVDWWKHGHILQLWHPDVVVSOLW
&RUUHODWLRQ EHWZHHQ WKH DYHUDJH QHXWURQ QXPEHUV DW WKH GHILQLWH PDVV VSOLW IRU D JLYHQ WRWDO NLQHWLF HQHUJ\ RI ILVVLRQ IUDJPHQWV PD\ EH FDOFXODWHG E\ WKHXVHRIWKHH[SHULPHQWDOGDWDRQQHXWURQDYHUDJH QXPEHUߥሺܣሻIRUWKHIUDJPHQWRIPDVVQXPEHUܣDW WRWDO NLQHWLF HQHUJ\ܧRI IUDJPHQWV SDLU E\ߥҧሺܣሻ
ZH GHQRWH DYHUDJH RI WKLV PHDQ QXPEHU RYHU WKH WRWDO NLQHWLF HQHUJ\ GLVWULEXWLRQ 7KH PHDVXUHG LQ WKH ZRUN >@ PHDQ YDOXHV RI QHXWURQ QXPEHU DUH GLVSHUVHG IURP WKH DYHUDJH OLJKW ܣൌ ͳͲͺ DQG
KHDY\ ܣுൌ ͳͶͶ IUDJPHQWV RI ZKLFK ߪఔಽDQG
ߪఔಹ DUHߪఔಽൌ ͲǤ͵ͻǡ ߪఔಹൌ ͲǤͺ͵ʹ DW WKH PRVW
SUREDEOH WRWDO NLQHWLF HQHUJ\ ܧൌ ͳͻͲܯܸ݁
&RUUHVSRQGLQJ FRYDULDQFH ܿݒሺߥǡ ߥுሻ DQG
FRUUHODWLRQ FRHIILFLHQWߩሺߥǡ ߥுሻ RI WKHVH QHXWURQ
QXPEHUV DUH ܿݒሺߥǡ ߥுሻ ൌ െͲǤ͵ͺǡ ߩሺߥǡ ߥுሻ ൌ
െͲǤͳͶǤ7KLV UHVXOW PHDQV WKDW WKHUH LV VLJQLILFDQW DQWL FRUUHODWLRQ EHWZHHQ WKH H[FLWDWLRQ HQHUJ\ RI KHDY\ DQG OLJKW IUDJPHQWV LH WKH KLJKHU WKH H[FLWDWLRQ HQHUJ\ RI RQH IUDJPHQW WKH ORZHU WKH RQH RI DQRWKHU IUDJPHQW DW WKH IL[HG WRWDO NLQHWLF HQHUJ\ RI IUDJPHQW SDLU +RZHYHU RQH RI PRVW LPSRUWDQWFKDUDFWHULVWLFVXVHGLQPDQ\DSSOLFDWLRQV RI SURPSW ILVVLRQ QHXWURQ VSHFWUXP LV WKH FRUUHODWLRQ FRHIILFLHQW DW DOO SRVVLEOH ILVVLRQ IUDJPHQW NLQHWLF HQHUJLHV LH FRUUHODWLRQ DW WKH GHILQLWHPDVVVSOLW
7KH FRUUHODWLRQ FRHIILFLHQW DW WKH DYHUDJH PDVV VSOLW ܣൌ ͳͲͺǡ ܣுൌ ͳͶͶ LQ WKH VSRQWDQHRXV
ILVVLRQ RIଶହଶܥ݂PD\ EH FDOFXODWHG E\ WKH XVH RI H[SHULPHQWDOGDWDIRUWKHDYHUDJHQHXWURQQXPEHU GHSHQGHQW RQ WKH ILVVLRQ IUDJPHQW WRWDO NLQHWLF HQHUJ\ )LJ DQG IRU WKH WRWDO NLQHWLF HQHUJ\ GLVWULEXWLRQሺܧሻRIWKLVIUDJPHQWSDLU)LJ>@
)LJ ([SHULPHQWDO DYHUDJH QHXWURQ YDOXHVߥ
VROLGFXUYHDQGߥுGDVKHGFXUYHGHSHQGHQWRQ WKHWRWDONLQHWLFHQHUJ\RIILVVLRQIUDJPHQWVIRUWKH $YHUDJH QHXWURQ QXP EHUV Ȟ/ DQG Ȟ+ 7RWDONLQHWLFHQHUJ\(.0H9 8
PDVV VSOLW $/ $+ LQ WKH VSRQWDQHRXV ILVVLRQRI&I>@
7KH FRYDULDQFH DQG WKH FRUUHODWLRQ LQ WZR GLVFUHWH VHW RI YDULDEOHV൛ߥൟDQG൛ߥுൟKDYLQJ GLVWULEXWLRQV
RUSUREDELOLWLHVሺߥሻDQGሺߥுሻDUH>@
ܿݒሺߥǡ ߥுሻ ൌσ ൫ߥ െ ߥҧ൯൫ߥு െ ߥҧு൯൫ߥ൯൫ߥு൯
ߩሺߥǡ ߥுሻ ൌఙమ௩ሺఔሺఔಽሻఙಽమǡఔሺఔಹಹሻሻ
ZKHUH GLVSHUVLRQߪ DQG DYHUDJH QXPEHU ߥҧ DUH GHWHUPLQHGE\ ߪଶ൫ߥ ǡு൯ ൌ σ ൫ߥǡு െ ߥҧǡு൯ ଶ ൫ߥǡு ൯ ǡ ߥҧǡுൌ σ ߥ ǡு ሺߥǡு ሻ
IRU WKH OLJKW IUDJPHQWܮ DQG KHDY\ IUDJPHQW ܪ VHSDUDWHO\ 1HXWURQ \LHOG GHSHQGHQW RQ WRWDO NLQHWLFHQHUJ\LQWKHDERYHIRUPXODHLVWKHVDPHDV WKH WRWDO NLQHWLF HQHUJ\ \LHOG൫ߥ൯ ൌ ൫ߥு൯ ൌ
ሺܧሻ DQG LV QRUPDOL]HG DV σ ൫ߥଵ଼ ǡு ൯ ൌ ͳͲͲ
LVWKHQXPEHURIH[SHULPHQWDOGDWDLQWKH)LJV
)LJ([SHULPHQWDOWRWDONLQHWLFHQHUJ\GLVWULEXWLRQ
RI WKH SDLU RI ILVVLRQ IUDJPHQWV LQ VSRQWDQHRXV ILVVLRQRI&IIRUWKHPDVVVSOLW$
/ $+ >@
7KH FDOFXODWHG YDOXHV IRU WKH DYHUDJH QHXWURQ QXPEHUV DUH IRXQG WR EH ߥҧൌ ͳǤͺͻǡ ߥҧுൌ
ͳǤǡZKLFKDUHYHU\FORVHWRWKHPHDVXUHGUHVXOWV ߥҧൌ ͳǤͺͺǡ ߥҧுൌ ͳǤͶ LQ WKH ZRUN >@ 1HXWURQ
QXPEHU GLVSHUVLRQV DQG FRUUHODWLRQ FRHIILFLHQW DUH IRXQG WR EHߪଶሺߥ
ሻ ൌ ͲǤͺͷǡ ߪଶሺߥுሻ ൌ ͲǤͻDQG
ߩሺߥǡ ߥுሻ ൌ ͲǤͲ͵Ͳ UHVSHFWLYHO\ &RUUHODWLRQ
FRHIILFLHQW PHDVXUHG LQ WKH ZRUN >@ KDV YDOXH RI ߩ௫൫ߥǡߥு൯ ൌ െͲǤͲͶ WKH VWDWLVWLFDO H[SHULPHQWDO
HUURU RI ZKLFK LV 7KXV WKH FDOFXODWHG YDOXH DJUHHV ZHOO ZLWK WKLV YDOXH 7KLV UHVXOW LQGLFDWHV
WKDW WKHUH LV D QHJOLJLEOH FRUUHODWLRQ EHWZHHQ WKH DYHUDJH QHXWURQ QXPEHUV IURP FRPSOHPHQWDU\ ILVVLRQ IUDJPHQWV ZKHQ RQH LQWHJUDWH RYHU WRWDO NLQHWLF HQHUJ\ GLVWULEXWLRQ RI IUDJPHQW SDLU ,Q WHUPVRIWKHH[FLWDWLRQHQHUJLHVWKHUHLVDOPRVW]HUR FRUUHODWLRQ EHWZHHQ WKH H[FLWDWLRQ HQHUJLHV RI IUDJPHQW SDLU $SSDUHQWO\ WKLV UHVXOW PHDQV WKDW LQGHSHQGHQW H[FLWDWLRQ HQHUJ\ GLVWULEXWLRQ LQ WKH DYHUDJH OLJKW DQG KHDY\ ILVVLRQ IUDJPHQW SDLU LV YDOLG IRU RWKHU IUDJPHQW SDLUV DQG LW LV YHU\ LPSRUWDQWLQFDOFXODWLRQRIQHXWURQHQHUJ\VSHFWUXP LQILVVLRQ>@
&RUUHODWLRQEHWZHHQWKHDYHUDJHQHXWURQ QXPEHUVRIKHDY\DQGOLJKWPDVVJURXSV
7KH DYHUDJH QXPEHU RI QHXWURQV HPLWWHG IURP WKH IUDJPHQW RI PDVVܣ DW DOO LWV SRVVLEOH NLQHWLF HQHUJLHV LV DQRWKHU LPSRUWDQW FKDUDFWHULVWLF LQ GHGXFLQJ WKH H[FLWDWLRQ HQHUJ\ SDUWLWLRQ EHWZHHQ WKH ILVVLRQ IUDJPHQWV +HUH ZH LQYHVWLJDWHG WKH JOREDO FKDUDFWHULVWLFFRUUHODWLRQ LQ DYHUDJH QHXWURQ QXPEHUV LQFOXGLQJ DOO FRPSOHPHQWDU\ ILVVLRQ IUDJPHQW PDVVHV LUUHVSHFWLYH WR WKHLU WRWDO NLQHWLF HQHUJLHV7KHFRHIILFLHQWLVGHWHUPLQHGDV
ߩ ൌ σ ቂఔഥሺ ಽሻିఔഥഥሺಽሻቃቂതሺౄିതതሺౄሻቃ ൜σ ൣఔഥሺ ಽሻିఔഥഥሺಽሻ൧మσ ൣఔഥ൫ ಹ൯ିఔഥഥሺಹሻ൧మൠభ మΤ
ZKHUHߥҧሺܣሻ DQG ߥҧሺܣுሻ DUH WKH DYHUDJH QHXWURQ
QXPEHUV RI݅WK FRPSOHPHQWDU\ ILVVLRQ IUDJPHQWV ܣDQG ܣு UHVSHFWLYHO\ ([SHULPHQWDO GDWD RI WKH
ZRUN >@ IRU WKLV TXDQWLW\ DUH LOOXVWUDWHG LQ WKH )LJߥҧҧሺܣሻ DQG ߥҧҧሺܣுሻ DUH WKH DYHUDJH QHXWURQ
QXPEHUV LQ WKH OLJKW DQG KHDY\ IUDJPHQWV JURXS UHVSHFWLYHO\DQGDUHGHWHUPLQHGE\ ߥҧҧሺܣሻ ൌσ ఔഥሺಽ ሻ ಿ ே ߥҧҧሺܣுሻ ൌ σ ఔഥሺಿ ಹሻ ே ܰLVWKHQXPEHURIIUDJPHQWVLQHDFKJURXS :H GLYLGH WKH ZKROH PDVV UDQJH RI ILVVLRQ IUDJPHQWV LQWR WKUHH JURXSVPDVV UDQJHV VXEVWDQWLDWLQJ WKH PRQRWRQLFDOO\ EHKDYLRU RYHUORRNHG LQ WKH PDVV GLVWULEXWLRQ RI ILVVLRQ IUDJPHQW LQ WKH VSRQWDQHRXV ILVVLRQ RIଶହଶܥ݂> @7KHVHWKUHHPDVVUDQJHVDUH Dܣሺ͵ െ ͳͲሻǡ ܣுሺͳͶ െ ͳͻሻ EܣሺͳͲ െ ͳͳʹሻǡ ܣுሺͳͶͲ െ ͳͶͷሻ Fܣሺͳͳʹ െ ͳʹሻǡ ܣுሺͳʹ െ ͳͶͲሻ 7RWDO NLQHWLF HQHUJ\ GLVWULEXWLRQ S( 7RWDONLQHWLFHQHUJ\(.0H9
Kourmoetal./JournalofNuclearSciences1(2014)6Ͳ12
)LJ ([SHULPHQWDO DYHUDJH QHXWURQ QXPEHU
GHSHQGHQWRQWKHILVVLRQIUDJPHQWPDVVQXPEHULQ WKHVSRQWDQHRXVILVVLRQRI&I>@
,Q WKH UDQJH D PDVV \LHOG RI FRPSOHPHQWDU\ IUDJPHQWV LV FRQWLQXRXVO\ LQFUHDVLQJ ZKHUHDV LQ WKHUDQJHFLWLVFRQWLQXRXVO\GHFUHDVLQJDQGLQWKH UDQJH E ILVVLRQ IUDJPHQW PDVV \LHOGV DUH DSSUR[LPDWHO\VDPHSUREDEOH
&DOFXODWHG FRUUHODWLRQ FRHIILFLHQWV DUH െͲǤ͵͵ǡ െͲǤͻͻͶǡ െͲǤͻͶͲLQ WKH PDVV UDQJHV D E DQG F UHVSHFWLYHO\ 7KH ORZHVW FRUUHODWLRQ FRHIILFLHQW LV IRXQG LQ WKH PDVV UDQJH E WKDW PHDQV DOPRVW FRPSOHWH DQWL FRUUHODWLRQ LQ WKH HPLWWHG IURP FRPSOHPHQWDU\ IUDJPHQWV QHXWURQ QXPEHUV$UHODWLYHO\VORZHUDQWLFRUUHODWLRQLQWKH PDVV UDQJH D LV GXH WR LUUHJXODULWLHV LQߥҧሺܣሻ EHKDYLRU LQ )LJ &RUUHODWLRQ FRHIILFLHQW HVWLPDWH IRUWKHZKROHPDVVUDQJHܣሺ͵ െ ͳʹሻǡ ܣுሺͳʹ െ
ͳͻሻ IUDJPHQW SDLU LV IRXQG WR EHെͲǤͺͺ͵ 1RWHWKDWH[SHULPHQWDOGDWDKDYHHUURUVͳͲ െ ͷͲΨ DW WKH PDVV QXPEHUV OHVV WKDQܣ ൌ ͺͲDQG KLJKHU WKDQܣ ൌ ͳʹ ,I QHXWURQ QXPEHU GDWD IRU WKHVH PDVVHV DUH H[FOXGHG WKHQ WKH FRHIILFLHQW RI FRUUHODWLRQFDOFXODWHGIRUWKHZKROHPDVVUDQJH IUDJPHQW SDLU KDV YDOXH RIߩ ൌ െͲǤͻͷ 7KHVH UHVXOWV VD\ WKDW WRWDO DYHUDJH QXPEHU RI QHXWURQV HPLWWHG E\ D SDLU RI IUDJPHQWV DSSUR[LPDWHO\ LV FRQVWDQW LQ DJUHHPHQW ZLWK WKH UHVXOW RI 7HUUHOO DQDO\VLV>@DQGZLWKWKHUHVXOWVRI>@,QGHHGWKH WRWDO DYHUDJH QXPEHU RI QHXWURQV ߥҧ௧௧ሺܣሻ ൌ
ߥҧሺܣሻ ߥҧுሺܣሻ LOOXVWUDWHG LQ )LJ YHUVXV OLJKW
IUDJPHQW PDVV FRQILUPV WKLV UHVXOW LQ WKH ILVVLRQ IUDJPHQW PDVV UDQJH LW LV VOLJKWO\ LQFUHDVLQJ VWDUWLQJ IURP PDVV XS WR PDVV DQGWKHQLVVOLJKWO\GHFUHDVLQJ
)LJ7RWDODYHUDJHQXPEHURIQHXWURQVGHSHQGHQW
RQWKHOLJKWIUDJPHQWPDVV
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ଶହଶܥ݂HYHQWKRXJKHQHUJ\ UHOHDVH LQ ILVVLRQ LV SDUWLFLSDWHG LQ WKH NLQHWLF HQHUJ\DQGH[FLWDWLRQHQHUJ\IRUPV,QRWKHUZRUGV WKHGLIIHUHQFHEHWZHHQWKHHQHUJ\UHOHDVHDQGWRWDO NLQHWLFHQHUJ\RIILVVLRQIUDJPHQWVIRUWKHGLIIHUHQW PDVV VSOLWV LV XQFKDQJHG +RZHYHU WKH HQHUJ\ RI WKH HPLWWHG SKRWRQV IURP ILVVLRQ IUDJPHQWV DQG DFFXUDWH YDOXH RI WKH H[FLWDWLRQ HQHUJ\ FDUULHG RXW E\ HPLWWHG QHXWURQ PXVW EH WDNHQ LQWR DFFRXQW DFFXUDWHO\ IRU WKH FDOFXODWLRQ RI WKH H[FLWDWLRQ HQHUJ\RIILVVLRQIUDJPHQWV
&DOFXODWLRQRIWKHDYHUDJHH[FLWDWLRQHQHUJ\RI WKHILVVLRQIUDJPHQWVDQGHQHUJ\SDUWLWLRQ EHWZHHQWKHFRPSOHPHQWDU\IUDJPHQWV
7R FDOFXODWH WKH FRUUHODWLRQ EHWZHHQ WKH DYHUDJH H[FLWDWLRQHQHUJLHVRIWKHFRPSOHPHQWDU\IUDJPHQWV ZH XVH WKH H[SUHVVLRQ IRU WKH H[FLWDWLRQ HQHUJ\ RI ILVVLRQIUDJPHQWDVLQ5HIV>@ ܧതൌ ߥҧሺܣሻ ሾܤതሺܣሻ ߝҧሺܣሻሿ ܧതఊሺܣሻǤ 0 1 2 3 4 5 $YHUDJH QHXWURQ QXP EHU 0DVVQXPEHU$ 7RWDODYHUDJH QXP EHURI QHXWURQV 0DVVQXPEHU$ 10
+HUHܤത LV WKH QHXWURQ ELQGLQJ HQHUJ\ DYHUDJHG
RYHU WKH FDVFDGH QHXWURQ HPLVVLRQ DQG FKDUJH GLVWULEXWLRQ IRU WKH ILVVLRQ IUDJPHQW RI PDVV ߝҧሺܣሻLV WKH HPLWWHG QHXWURQ DYHUDJH HQHUJ\ LQ WKH FHQWHURIPDVVV\VWHPRIILVVLRQIUDJPHQWܧതఊሺܣሻLV
WKHDYHUDJHHQHUJ\RIWKHJDPPDTXDQWXPHPLWWHG IURP IUDJPHQW RI PDVVܣ 7KH ߥҧሺܣሻ DQG ߝҧሺܣሻ YDOXHV DUH WDNHQ IURP >@ :H XVH WKH HVWLPDWLRQ JLYHQ LQ ZRUN >@ IRU WKH DYHUDJH QHXWURQ ELQGLQJ HQHUJ\ܤതሺܣሻRI ILVVLRQ IUDJPHQW RI PDVV QXPEHU
ܣ0HDQJDPPDHQHUJ\LVFDOFXODWHGE\WKHXVHRI WKHH[SUHVVLRQ>@ ܧതఊሺܣሻ ൌ ൬Ǥͺ െ ͲǤͳͷͷͺ మ ൰ ή ߥҧሺܣሻ ሺͲǤͳͳͳʹమ െ ʹǤʹͶͲͺሻܯܸ݁ IRUDILVVLRQQXFOHXVRIFKDUJHQXPEHUܼDQGPDVV QXPEHUܣ7KLVUHGXFHVWRWKHH[SUHVVLRQ>@ ܧതఊ؆ ሾͲǤͷߥҧሺܣሻ ʹሿܯܸ݁
IRU &I VSRQWDQHRXV ILVVLRQ ZKLFK LV WKH DSSUR[LPDWLRQ XVHG LQ GHVFULSWLRQ RI WKH H[SHULPHQWDOGDWDVHH>@%HKDYLRURIܧതఊሺܣሻDVD
IXQFWLRQRIܣLVVLPLODUWRWKHEHKDYLRURIRIߥҧሺܣሻ 7KH UHVXOWV RI WKH FDOFXODWLRQV RI WKH DYHUDJH H[FLWDWLRQ HQHUJ\ LQ WKH PDVV UDQJH DUH VKRZQLQ)LJVROLGFXUYHH[SHULPHQWDOGDWDIRU ߝҧሺܣሻDYDLODEOH LQ ZRUN >@ VWDUWV DWܣ ൌ ͺͻ 7KH FDOFXODWLRQ UHVXOW RI ZRUN >@ GDVKHG FXUYH EDVHGRQDQDVVXPSWLRQWKDWWRWDOH[FLWDWLRQHQHUJ\ LV SDUWLWLRQHG EHWZHHQ WKH ILVVLRQ IUDJPHQWV LQ WKH VDPH UDWLR DV WKH QXPEHUV RI SURPSW QHXWURQV HPLWWHG E\ WKHVH IUDJPHQWV LV DOVR VKRZQ LQ WKLV ILJXUH 6RPH GLVFUHSDQF\ LV VHHQ LQ WKH KHDYLHVW PDVV UHJLRQV RI WKH OLJKW DQG KHDY\ ILVVLRQ IUDJPHQWV
7KH FRUUHODWLRQ EHWZHHQ WKH DYHUDJH H[FLWDWLRQ HQHUJLHV RI FRPSOHPHQWDU\ ILVVLRQ IUDJPHQWV LV FDOFXODWHGOLNHWKHFRUUHODWLRQFRHIILFLHQWLQQHXWURQ DYHUDJH PXOWLSOLFLW\ VHH (T DQG LWV YDOXH LV െͲǤͺͷͷ :H VHH WKDW WKH DQWL FRUUHODWLRQ EHWZHHQ WKH H[FLWDWLRQ HQHUJLHV LV ORZHU WKDQ WKDW IRU DYHUDJHQHXWURQQXPEHUVFRPSDUHGWRെͲǤͻͷ
)LJ $YHUDJH H[FLWDWLRQ HQHUJ\ RI ILVVLRQ
IUDJPHQWV GHSHQGHQW RQ WKH IUDJPHQW PDVV FDOFXODWHGE\WKHXVHRI(TVVROLGFXUYHLQ FRPSDULVRQZLWKWKHFDOFXODWLRQUHVXOWRIWKHZRUN >@GDVKHGFXUYH
7KH UDWLR RI ILVVLRQ IUDJPHQW H[FLWDWLRQ HQHUJ\ WR WKH WRWDO H[FLWDWLRQ HQHUJ\ RI FRPSOHPHQWDU\ IUDJPHQWV LV DQRWKHU FKDUDFWHULVWLF RI H[FLWDWLRQ HQHUJ\SDUWLWLRQEHWZHHQWKHILVVLRQIUDJPHQWV7KLV UDWLRKDVWKHIRUP
ܴ ൌாതሺಽሻ
ாത
:H FDOFXODWH WRWDO H[FLWDWLRQ HQHUJ\ IURP WKH UHODWLRQ ܧത௧௧ൌ ܧതሺܣሻ ܧതሺܣுሻ DQGWKHUHVXOWLVJLYHQLQ)LJ )LJ$YHUDJHWRWDOH[FLWDWLRQHQHUJ\RIWKHSDLURI ILVVLRQIUDJPHQWVGHSHQGHQWRQWKHOLJKWIUDJPHQW PDVVFDOFXODWHGE\WKHXVHRI(TV 7KH WRWDO DYHUDJH H[FLWDWLRQ HQHUJ\ RI FRPSOHPHQWDU\ ILVVLRQ IUDJPHQWV LV IRXQG LQ WKH UDQJHʹͺ െ ͵Ͳܯܸ݁ LQ WKH OLJKW IUDJPHQW PDVV UDQJH7KHQLWLQFUHDVHVXSWR͵ͻܯܸ݁DW WKHPDVVQXPEHUܣ ൌ ͳʹʹKDYLQJPD[LPXPYDOXH DQG WKHQ GHFUHDVHV WR WKH YDOXH RI͵ͷܯܸ݁DW WKH V\PPHWULF PDVV VSOLW 7KH LQFUHDVH LQ WKH WRWDO H[FLWDWLRQHQHUJ\VWDUWLQJRIWKHPDVVLVGXHWR $YHUDJH H[FLWDWLRQ HQHUJ\ 0H9 0DVVQXPEHU$ 7RWDO DYHUDJH H[FLWDWLRQ HQHUJ\ 0H9 0DVVQXPEHU$
Kourmoetal./JournalofNuclearSciences1(2014)6Ͳ12
WKH LQFUHDVH RI DOO IDFWRUVWRWDO DYHUDJH QXPEHU RI QHXWURQV QHXWURQ DYHUDJH ELQGLQJ HQHUJ\ DQG QHXWURQ DYHUDJH HQHUJ\ LQ WKH FHQWHU PDVV V\VWHP 7KHVH UHVXOWV PD\ EH FRPSDUHG ZLWK WKH H[SHULPHQWDOGDWDRIZRUN>@RQͳʹܯܸ݁SURWRQ LQGXFHG ILVVLRQ RI232Th UHODWHG ZLWK DV\PPHWULF
ILVVLRQ PRGH RI FRPSRXQG V\VWHP ଶଷଶ݄ܶ ,Q ZRUN >@ WKH PHDVXUHG DYHUDJH WRWDO H[FLWDWLRQ HQHUJ\ IRU DV\PPHWULF ILVVLRQ PRGH KDV YDOXHV UDQJLQJ EHWZHHQ ሺʹͺ െ ͵ʹሻܯܸ݁ LQ WKH OLJKW IUDJPHQW PDVV UDQJH 7KLV UHVXOW LV LQ DJUHHPHQW ZLWK RXU FDOFXODWLRQ UHVXOW IRU WKH PDVV UDQJH$WKLJKHUPDVVHVWKHH[SHULPHQWDO GDWDLOOXVWUDWHDWܣ ͳͲͲVLPLODUEHKDYLRULQWRWDO H[FLWDWLRQHQHUJ\
)LJ7KHUDWLR5RIWKHILVVLRQIUDJPHQWDYHUDJH
H[FLWDWLRQ HQHUJ\ WR WKH WRWDO DYHUDJH H[FLWDWLRQ HQHUJ\RIFRPSOHPHQWDU\IUDJPHQWVYHUVXVWKHOLJKW IUDJPHQWPDVVFDOFXODWHGE\WKHXVHRI(TV 7KHUHVXOWRIWKHFDOFXODWLRQRIWKHUDWLRܴJLYHQE\ (TVLVVKRZQLQ)LJ$VLWLVVHHQLQWKH ILJXUH VWDUWLQJ ZLWK OLJKW IUDJPHQW PDVVܣ ൌ ͳͲ XS WR V\PPHWULF PDVV VSOLW DW ܣ ൌ ͳʹ OLJKW IUDJPHQWV FDUU\ RXW H[FLWDWLRQ HQHUJ\ KLJKHU WKDQ WKH KHDY\ IUDJPHQW ሺܴ ͳȀʹሻ ZKHQ ͺͷΨ PD[LPXP VKDUH RI WKH WRWDO H[FLWDWLRQ FRPHV WR WKH OLJKW IUDJPHQW DW $ +RZHYHU WKLV PHDQV WKDWDWWKLVPDVVQXPEHUWKHUHODWLRQ
ͳ െ ܧതሺܣሻ ܧതΤ ௧௧ൌ ܧതሺܣுሻ ܧതΤ ௧௧
EHFRPHV PLQLPXP LH KHDY\ IUDJPHQW RI PDVV ܣ ൌ ͳ͵Ͳ FDUULHV ͳͷΨ RI WRWDO H[FLWDWLRQ HQHUJ\ *HQHUDOO\ LQ WKH ILVVLRQ IUDJPHQW PDVV UDQJH ሺͺͻ െ ͳʹʹሻWKHUDWLRܴLVJUDGXDOO\DSSUR[LPDWHO\ OLQHDUO\ LQFUHDVLQJ ZLWK WKH DYHUDJH VORSH RI ͲǤͲͳͺǤ7KLV VORSH LQ ZRUN >@ ZDV IRXQG WR EH
ͲǤͲʹ
'LVFXVVLRQDQGFRQFOXVLRQ
7KH SDUWLWLRQ RI WKH H[FLWDWLRQ HQHUJ\ EHWZHHQ WKH IUDJPHQWSDLULQWKHVSRQWDQHRXVILVVLRQRIଶହଶܥ݂LV LQYHVWLJDWHGLQWHUPVRIWKHFRUUHODWLRQFRHIILFLHQWV EHWZHHQ WKH DYHUDJH QHXWURQ QXPEHU LQWHJUDWHG RYHU WKH WRWDO NLQHWLF HQHUJ\ GLVWULEXWLRQ RI ILVVLRQ IUDJPHQWV DW WKH GHILQLWH PDVV VSOLW DQG EHWZHHQ WKH QHXWURQ DYHUDJH QXPEHU IURP FRPSOHPHQWDU\ IUDJPHQWV LQ D ZKROH PDVV GLVWULEXWLRQ UDQJH RI ILVVLRQ IUDJPHQWV ,W LV VKRZQ WKDW WKHUH H[LVWV DSSUR[LPDWHO\]HURFRUUHODWLRQEHWZHHQWKHQHXWURQ QXPEHUVDWWKHGHILQLWHPDVVVSOLWFRUUHVSRQGLQJWR WKHDYHUDJHOLJKWDQGKHDY\IUDJPHQWPDVVHVܣൌ ͳͲͺǡ ܣுൌ ͳͶͶǤ,QWHUPVRIWKHH[FLWDWLRQHQHUJ\ WKLV PHDQV WKDW WKH H[FLWDWLRQ HQHUJLHV LQ FRPSOHPHQWDU\IUDJPHQWVLQILVVLRQDUHGLVWULEXWHG LQGHSHQGHQWO\ 7KLV IDFW LV XVHG IRU FODFXODWLRQ RI WKH SURPSW ILVVLRQ QHXWURQ VSHFWUD >@ :KHUHDV WKHUH LV DSSUR[LPDWHO\ FRPSOHWH DQWL FRUUHODWLRQ EHWZHHQ WKH DYHUDJH QHXWURQ QXPEHUV LQFOXGLQJ DOO ILVVLRQ IUDJPHQW PDVVHV 7KLV PHDQV WKDW WKH HTXDWLRQߥҧ ߥҧுൌ ܿ݊ݏݐǤDSSUR[LPDWHO\
KROGV WKURXJK WKH ZKROH ILVVLRQ IUDJPHQW PDVV UDQJH
7KH FRUUHODWLRQ EHWZHHQ WKH H[FLWDWLRQ HQHUJLHV RI FRPSOHPHQWDU\ ILVVLRQ IUDJPHQWV FDOFXODWHG LQ D ZKROH PDVV UDQJH EHFRPHV ZHDNHU FRPSDUHG WR WKDW RI LQ QHXWURQ DYHUDJH QXPEHU EHFDXVH RI LQIOXHQFH RI ERWK WKH QHXWURQ DYHUDJH ELQGLQJ HQHUJ\ DQG WKH QHXWURQ DYHUDJH FHQWHU RI PDVV HQHUJ\ ,Q IDFW WKH FRUUHODWLRQ FRHIILFLHQW IRU WKH H[FLWDWLRQHQHUJLHVLVെͲǤͺͷͷ
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
5HIHUHQFHV
>@ -7HUUHOO ³1HXWURQ \LHOGV IURP LQGLYLGXDO ILVVLRQ IUDJPHQWV´3K\V5HY 5DWLR5 0DVVQXPEHU$ 12
>@ +5%RZPDQ -&' 0LOWRQ 6*7KRPSVRQ DQG :-6ZLDWHFNL ´)XUWKHU VWXGLHV RI WKH SURPSW QHXWURQV IURP WKH VSRQWDQHRXV ILVVLRQ RI&I´ 3K\V 5HY
>@ +1LIHQHFNHU -)UHKDXW DQG 06ROHLOKDF´(WXGH GH O¶HPLVVLRQ QHXWURQLTXH GHV IUDJPHQWV GH ILVVLRQ GX FDOLIRUQLXP HQ IRQFWLRQ GH OHXU FKDUJH´ ³6WXG\ RI WKH QHXWURQ HPLVVLRQ RI FDOLIRUQLXP IUDJPHQWV DV D IXQFWLRQ RI WKHLU FKDUJH´ LQ 3URFHHGLQJV RI 6HFRQG ,QWHUQDWLRQDO $WRPLF (QHUJ\ $JHQF\ 6\PSRVLXP RQ 3K\VLFV DQG &KHPLVWU\ RI )LVVLRQ -XOD\$XJXVW 9LHQQD$XVWULD,$($9LHQQD >@09%OLQRY10.D]DULQRY,7.ULV\XNDQG66 .RYDOHQNR6RY-1XFO3K\VUHIHUHQFH LVLQGLFDWHGLQZRUN>@ >@$*DYURQ=)UDHQNHO3K\V/HWW% UHIHUHQFHLVLQGLFDWHGLQZRUN>@ >@ 59DQGHQERVFK -5 +XL]HQJD ³1XFOHDU )LVVLRQ´ $FDGLPLF3UHVV1HZ<RUNDQG >@ +1LIHQHFNHU &6LJQDUELHDX[ 5%DELQHW - 3RLWRX ´1HXWURQDQGJDPPDHPLVVLRQLQILVVLRQ´LQ3URFHHGLQJV RI ,QWHUQDWLRQDO $WRPLF (QHUJ\ $JHQF\ 6\PSRVLXP RQ 3K\VLFV DQG &KHPLVWU\ RI )LVVLRQ $XJXVW 5RFKHVWHU1HZ<RUN,$($9LHQQD
>@ &6LJQDUELHDX[ 5%DELQHW +1LIHQHFNHU - 3RLWRX ´(WXGHH[SHULPHQWDOHGHODFRUUHODWLRQHQWUHOHVQRPEUHV GH QHXWURQV SURPSWV HPLV SDU OHV GHX[ IUDJPHQWV FRPSOHPHQWDULHV GDQV OD ILVVLRQ VSRQWDQHH GH
&I´³([SHULPHQWDOVWXG\RIWKHFRUUHODWLRQEHWZHHQWKH
QXPEHUV RI SURPSW QHXWURQV HPLWWHG E\ WKH WZR FRPSOHPHQWDU\ IUDJPHQWV LQ VSRQWDQHRXV ILVVLRQ RI
&I´ LQ 3URFHHGLQJV RI ,QWHUQDWLRQDO $WRPLF (QHUJ\
$JHQF\ 6\PSRVLXP RQ 3K\VLFV DQG &KHPLVWU\ RI )LVVLRQ $XJXVW 5RFKHVWHU 1HZ <RUN ,$($9LHQQD
>@ &%XGW]-RUJHQVHQ DQG ..QLWWHU ³6LPXOWDQHRXV LQYHVWLJDWLRQ RI ILVVLRQ IUDJPHQWV DQG QHXWURQV LQ&I
6)´1XFO3K\V$
>@-38QLN-(*LQGOHU/(*HOHQGHQLQ.))O\QQ $*RUVNL 5. 6MREORP ³)UDJPHQW PDVV DQG NLQHWLF HQHUJ\ GLVWULEXWLRQV IRU ILVVLRQLQJ V\VWHPV UDQJLQJ IURP PDVVWR´LQ3URFHHGLQJVRI,QWHUQDWLRQDO$WRPLF (QHUJ\$JHQF\6\PSRVLXPRQ3K\VLFVDQG&KHPLVWU\RI )LVVLRQ$XJXVW5RFKHVWHU1HZ<RUN ,$($9LHQQD
>@ +0DUWHQ $5XEHQ DQG '6HOOLJHU ´)LVVLRQ IUDJPHQWV DQG SURPSW QHXWURQ HPLVVLRQ´ LQ 3URFFHGLQJ RI &RQVXOWDQW 0HHWLQJ RI ,QWHUQDWLRQDO $WRPLF (QHUJ\ $JHQF\RQ3K\VLFVRI1HXWURQ(PLVVLRQLQ)LVVLRQ0D\ 0LWR-DSDQ
>@ ,1LVKDQDND <1DJDPD + /NH]RH 0 7DQLNDZD </ =KDR . 6XHNL DQG + 1DNDKDUD ³3DUWLWLWLRQ RI WRWDO H[FLWDWLRQ HQHUJ\ EHWZHHQ IUDJPHQW SDLUV LQ DV\PPHWULFDQGV\PPHWULFILVVLRQPRGHV´3K\V5HY&
>@ 6/HPDULH 37DORX 7.DYDQR '*0DGODQG DQG 0%&KHGZLFN´&RUUHODWHGQHXWURQHPLVVLRQLQILVVLRQ´ ,QWHUQDWLRQDO &RQIHUDQFH IRU 1XFOHDU 'DWD IRU 6FLHQFH DQG 7HFKQRORJ\ $PHULFDQ ,QVWLWXWH RI 3K\VLFV ;
>@ &0DQDLOHVFNX $7XGRUD )-+DPEVFK &0RUDULX 62EHUVWHGW ³3DUWLWLLWLRQ RI WKH WRWDO H[FLWDWLRQ HQHUJ\ EHWZHHQ FRPSOHPHQWDU\ IUDJPHQWV³arxiv.org/pdf/1103.1574 DU;LY >QXFOWK@
>@ 16KX 7/LX <&KHQJ 1D =KHQJ ³3ODQ RI WKH 3)16FDOFXODWLRQZLWK6HPL(PSLULFDO0RGHODQG6WXG\ RI WKH HQHUJ\ SDUWLWLRQ´ 6XPPDU\ 5HSRUW RI )LUVW 5HVHDUFK &RRUGLQDWLRQ 0HHWLQJ RQ 3URPSW )LVVLRQ 1HXWURQ 6SHFWUD RI 0DMRU $FWLQLGHV $SULO ,$($ +HDGTXDUWHUV9LHQQD$XVWULD
>@ +0$KPDGRY %*|QO 0<LOPD] ³3URPSW 1HXWURQ 6SHFWUXP DQG $YHUDJH 1HXWURQ 0XOWLSOLFLW\ ,Q 6SRQWDQHRXV )LVVLRQ RI &I´, 3K\V 5HY &
>@ $99RLQRY %02JLQQL 60*ULPHV HW DO ³1XFOHDU H[FLWDWLRQV DW FRQVWDQW WHPSHUDWXUH´ 3K\VLFDO 5HYLHZ&5
>@ %-XUDGR.+6FKPLGW ³([FLWDWLRQHQHUJ\ VRUWLQJ LQ VXSHU IOXLG ILVVLRQ G\QDPLFV´ (3- :HE RI &RQIHUHQFHV
>@ .DUO+HLQ] 6FKPLGW DQG %RHWUL] -XUDGR ³)LQDO H[FLWDWLRQ HQHUJ\ RI ILVVLRQ IUDJPHQWV´ 3K\V5HY&
>@ $(6DYHOHY 93*RUHORY %0'MXED ³&RPSHWLWLRQ LQ SURPSW QHXWURQ DQG JDPPD HPLVVLRQ IURP ILVVLRQ IUDJPHQWV´ 6RY - 1XFO 3K\V
>@ *$&RUQ 70&RUQ ³0DWKHPDWLFDO +DQGERRN´ 0N*UDZ+LOO1HZ<RUN
>@ ' * 0DGODQG DQG - 5 1L[ ³1HZ FDOFXODWLRQ RI SURPSWILVVLRQQHXWURQVSHFWUDDQG DYHUDJH SURPSW QHXWURQ PXOWLSOLFLW\´ 1XFO 6FL (QJ
>@ -7HUUHOO ´)LVVLRQ QHXWURQ VSHFWUD DQG QXFOHDU WHPSHUDWXUHV´3K\V5HY
/RQGRQ